Sun Aile, Wang Yinqiao, Chen Yangrui, Shang Jin, Zheng Jie, Yu Shuchang, Su Siyuan, Sun Xulai, Zhang Jie
School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
Soft Matter. 2022 Feb 2;18(5):983-989. doi: 10.1039/d1sm01516h.
We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra () ∝ and, more severely, the longitudinal velocity power spectra () ∝ are affected by the prominent peak centered around ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of (the subscript '' refers to either T or L), we subsequently analyze the second-order velocity structure functions of (2)ν() in real space, which show the power-law scalings of (2)ν() ∝ for both modes. From the values of , we deduce the corresponding from the scaling relations of = + 2. The deduced values of increase continuously with the shear amplitude , showing no signature of yielding transition, and are slightly larger than = 2.0 at the limit of → 0, which corresponds to the elastic limit of the system, for all . The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.
我们进行了一项系统的实验研究，以探究在一系列剪切振幅的循环剪切作用下，低摩擦系数和高摩擦系数的二维颗粒物质中的速度波动情况。其速度场呈现出显著的类似湍流的特征，存在不同尺度的涡旋。与实际湍流不同，由于硬颗粒性质的静态结构因子，横向速度功率谱（）∝ 以及更显著的纵向速度功率谱（）∝ 的标度行为受到粒子间距离约为2π处的突出峰值的影响。为了将强峰值效应降低到（下标“”表示T或L）的实际值，我们随后在实空间中分析了（2）ν（）的二阶速度结构函数，这两种模式下的（2）ν（）均呈现出（2）ν（）∝ 的幂律标度。根据的值，我们从 = + 2的标度关系中推导出相应的。推导得到的值随着剪切振幅的增加而持续增大，未显示出屈服转变的特征，并且在 → 0的极限情况下，对于所有情况，均略大于 = 2.0，这对应于系统的弹性极限。颗粒间摩擦系数对类似湍流的速度波动没有显著影响。我们的研究结果表明，在循环剪切的颗粒材料中，类似湍流的集体颗粒运动受弹性和塑性共同支配。
